Factor: $$ 8+x^{3} $$ A $$ (2+x)\left(4-2 x+x^{2}\right) $$ B $$ (2+x)^{3} $$ C $$ (2-x)\left(4+2 x+x^{2}\right) $$ D $$ (2+x)\left(4+x^{2}\right) $$

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UpStudy AI · Accepted Answer

To factor the expression $$ 8 + x^{3} $$, let's analyze each of the provided options:

1. **Standard Factoring of Sum of Cubes:**
   The sum of cubes formula is:
   $$
   a^3 + b^3 = (a + b)(a^2 - ab + b^2)
   $$
   Applying this to $$ 8 + x^3 $$:
   $$
   8 + x^3 = 2^3 + x^3 = (2 + x)(4 - 2x + x^2)
   $$
   This matches **Option A**.

2. **Evaluating Other Options:**
   - **Option B: $$ (2 + x)^3 $$**
     $$
     (2 + x)^3 = 8 + 12x + 6x^2 + x^3 \neq 8 + x^3
     $$
   - **Option C: $$ (2 - x)(4 + 2x + x^2) $$**
     $$
     (2 - x)(4 + 2x + x^2) = 8 - x^3 \neq 8 + x^3
     $$
   - **Option D: $$ (2 + x)(4 + x^2) $$**
     $$
     (2 + x)(4 + x^2) = 8 + 2x^2 + 4x + x^3 \neq 8 + x^3
     $$

**Conclusion:**
The correct factorization of $$ 8 + x^3 $$ is:

**Answer:**  
**A** $$ (2 + x)\left(4 - 2x + x^{2}\right) $$
The correct factorization is $$ (2 + x)(4 - 2x + x^{2}) $$.

Factor:
A
B
C
D

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Factor: A B C D